This invention relates to a method for restoring missing or noisy seismic traces to a seismic record. This invention further relates to extrapolating traces beyond the edges of a seismic record.
In seismic exploration, it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone location to obtain a collection of seismic traces, commonly referred to as a seismic record. When the vibrations so recorded are caused by a seismic source activated at a known time and location, the seismic record can be processed by a computer in known ways to produce an image of the subsurface. The image of the subsurface is commonly interpreted by geophysicists to detect the possible presence of valuable hydrocarbons.
Seismic traces are commonly recorded as digital samples representing the amplitude of received seismic signals as a function of time. Since seismic traces are usual obtained along a line of exploration on the surface of the earth, the digital samples can be formed into x-t arrays with each sample in the array representing the amplitude of the seismic signal as a function of horizontal distance and time. This collection of digital samples for one particular seismic source at one particular location is called a seismic record. When such seismic records are processed and visually reproduced, by plotting or the like, a seismic section is produced. A seismic section depicts the subsurface layering of a section of the earth. It is the principal tool which the geophysicist studies to determine the nature of the earth's subsurface formation. Before the seismic record can be converted into a seismic section for interpretation by geophysicists, the seismic record must be extensively processed to remove noise and to make reflection events discernible.
A common problem during seismic data acquisition is the presence of seismic traces with no recorded data or seismic traces that clearly contain severe noise contamination. For example, the failure of one of more geophones intended to collect data can result in a seismic trace without data. Standard practice among geophysicists faced with seismic traces with no recorded data or severely contaminated seismic traces has been to exclude such traces, commonly referred to as "null" traces, from the otherwise satisfactory data set. The collected seismic data would be processed normally without the excluded data.
Missing traces in seismic records may create noise when the data is processed. F-k filters used to remove large coherent noises, such as multiples and direct arrivals, create processing noise in the vicinity of the missing traces. Dip movement, another prestack process, creates processing noise where seismic events cross over null traces. In the slant stack domain null traces appear as linear noise, which may degrade the performance of other processes applied in this domain. Processing noise from missing traces may make reflection events less discernible, thereby adversely affecting prestack interpretation or interpretation of final stack sections. It is therefore desirable to restore missing traces before additional processing.
Various techniques have been applied to seismic records in an attempt to solve the problem of missing traces as described above. In U.S. Pat. No. 4,884,248 to Laster, Meek and Shirley, a seismic record is transformed into a data localizing space and muted to retain only the localized data components of the seismic record. The muted data is inverse-transformed into the x-t domain to produce first estimates of the seismic data to be restored. The first estimates of the restored data are substituted for the corresponding traces in the original seismic record. Fully restored traces corresponding to the missing or severely noise contaminated traces are determined from the single estimate of the restored traces.
In U.S. Pat. No. 4,860,265 to Shirley, Meek and Laster, a seismic record is transformed from the x-t domain to the f-k domain by a series of fast Fourier transforms. The f-k transform of the seismic record is filtered to retain only coherent events and the filtered transform is inverse-transformed back to the x-t domain. A first determination of the restored trace corresponding to the null trace is selected and substituted for the null trace. The first determination of the restored trace is used to determine a fully restored trace.
In U.S. Pat. No. 4,829,487 to Malloy, a null trace to be restored, as well as adjoining traces on each side of the null trace, are selected. A series of cross-correlations are determined for all points on the null trace. Restoration of data points is conducted by transforming the series of points of the adjacent traces corresponding to the maximum cross-correlation for the point into a Fourier representation, zero-padding the Fourier representation and producing a restored data point by inverse Fourier transforming the zero-padded data representation. The procedure is repeated for each point along the trace being restored. The procedure interpolates a trace between two original traces without altering the original data.